## Abstract

We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N -body density matrix. The body-fixed frame transformation is carried out in order to achieve an electron density that reflects the internal symmetry of the system. We discuss the implications of this body-fixed frame transformation and establish a Runge-Gross-type theorem and derive Kohn-Sham equations for the electrons and nuclei. We illustrate the formalism by performing calculations on a one-dimensional diatomic molecule for which the many-body Schrödinger equation can be solved numerically. These benchmark results are then compared to the solution of the time-dependent Kohn-Sham equations in the Hartree approximation. Furthermore, we analyze the excitation energies obtained from the linear response formalism in the single pole approximation. We find that there is a clear need for improved functionals that go beyond the simple Hartree approximation.

Original language | American English |
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Article number | 052514 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 76 |

Issue number | 5 |

DOIs | |

State | Published - 29 Nov 2007 |

Externally published | Yes |